Tropo-Scatter Link Budget Calculations

Tropospheric Scattering The Troposphere is the atmosphere below an upper limit called the tropo-pause, which is in a height of approx 10 km Above the tropo-pause the temperature is constant, there is little humidity and no movements in the air => few irregularities to scatter our radio signals Air is not uniform => eddies, thermals, turbulence etc. where the air has slightly different pressure and hence a different refractive index The effect of these irregularities on the wavefront is for the waves to be scattered and defocused

Tropospheric Scattering It is a very slight effect and Energy is scattered by very small angles, but over long paths this leads to Troposcatter propagation Signals may be scattered to receiver beyond the horizon For Troposcatter communication, the Common volume formed by the intersection of the antenna patterns is important

Tropospheric Scattering The common volume needs to be in the troposphere, so there is a limit to the propagation range The height of the troposphere differs between summer & winter and with latitude Higher the tropo-pause , higher are the nos. of scatter cell found and more the scatter can take place, greater the signal strength

Link Parameters and factors affecting Link Design Three parts of tropo-scatter path loss Free space loss from Tx antenna to horizon; d1 Tropo-scatter loss; (d-d1-d2) Free space loss from horizon to Rx antenna

Link Parameters and Factors affecting Link Design Transmitter: Tx Power, Tx antenna gain, Tx antenna height, Antenna elevation Channel: Climate, Carrier frequency, Distance, Relative separation of sites and horizon above sea level, Scatter angle, Scatter length, Annual mean refractivity, Height of the common volume, Crosspoint height and distance, Angular length, Symmetry factor, Diurnal , Zone on the earth … Receiver: Rx Power, Rx antenna gain, Rx antenna height, Antenna elevation, Rx noise floor, Rx Noise bandwidth, Rx Noise figure, Rx SNR, Diversity

Path Loss Estimation Value of transmission loss in dB, is given by L(dB) = 30 log(f) – 20 log(d) + f(θd) – V(de) Where, f = frequency in MHz, d = earth great circle distance f(θd) = attenuation function (dB) depending on product of scatter angle θ (rad) and path length d (km) V(de) = climate correction factor

Antenna Gain Calculation Antenna Gain for 2.4m dish = ~39 dBi Antenna gain = 20 log (Df/127.4) For parabolic dishes with 55% aperture efficiency; D meters, f MHz

Calculation of Antenna Gain Degradation Factor Effective Path antenna gain for 2.4 m dish = 72.5dBi Multi path coupling loss or ‘aperture to medium coupling loss’/ gain degradation factor Lgp = 25.8 – 0.29 (G1+G2) + 0.0036 (G1+G2)^2

Path geometry Ref.: Loss calculations by Approximative formulas from "Troposcatter Radio Links" (G Roda)

Link Budget System and path parameters Pt = 500 Watts LNA NF = 3 dB f = 5000 MHz d = 100 km B = 10 MHz h1 = 5 m h2 = 5 m d1 = 10 km d2 = 10 km h1‘ = 3 m h2‘ = 3 m % of time ‘q’= 99.9 Eb/N0 = 8 dB Data Rate = 10 Mbps SNR = 7 dB Case-1: Example Case-2: 2.4 m parabolic dish with indoor SSPA and Diplexer Case-3: 2.4 m parabolic dish with outdoor RF front end Case-1 Case-2 Case-3 Predicted Path loss for 99.9% availability 225 dB 225dB Effective Antenna Gain (GTX + GRX) 77 dBi 72 dBi RX Noise Figure 5 dB 4 dB 3 dB Rx Noise floor -100 dBm -102 dBm -104 dBm Rx signal strength for 500W TX power at each channel -92 dBm -97 dBm -96 dBm SNR after diversity combining (diversity gain ~7dB) 15 dB 12 dB 13 dB SNR Required (dB) for BER 1E-6 for QPSK 10 Mbps 7 dB Tropo Comm. Possible ? Yes

Link Budget Parameters Required terrain parameters: 1. The path distance, d, in kilometres which is determined from the great-circle calculations 2. The antenna heights (center of antenna feed) above ground, hg1 and hg2 , in kilometres 3. The elevation of the antenna sites in kilometres above mean sea level, eS1 and eS2 from maps or surveys => The heights of the antennas (center of antenna feed) above mean sea level, hS1 and hS2 in kilometres, are hS1 = hg1 + eS1 km hS2 = hg2 + eS2 km 4. The distances from the antenna sites to the radio horizons, dL1 and dL2 in kilometres from the path profile 5. The elevations of the radio horizons above mean sea level, hL1 and hL2 in kilometres 6. The horizon take-off angles Qe1 and Qe2 in radians 7. The angles a0 and B0 in radians

Link Budget Parameters Required terrain parameters: 8. The angular distance, Q , in radians = d/a +Qe1 +Qe2 [ a0 +B0 =Q] where d in km and a eff. earth radius 9. The distance between radio horizons, Ds, in kilometres 10. The parameter h0 h0 = s*d*Q / (1+ s)^2 11. The parameter s is the ratio of the angles a0 to B0 s = a0/B0 , if a0 < B0 B0/a0 otherwise 12. The effective antenna heights, he1’ and he2' in kilometres. These are estimated from the terrain profiles relative to a potential reflecting surface between the antenna site and its radio horizon. The effective antenna heights he1’ and he2’ are used primarily for determining the variability functions Y(q)

Link Budget Parameters Required atmospheric parameters. sea-level surface refractivity N0 (fig 4.4-2) Convert N0 to Ns Ns = N0 e^ (- 1057 * hs) hs is the elevation in km of each radio horizon above mean sea level, and the two values of Ns obtained in this manner are averaged in order to obtain the Ns applicable to a particular link. [exception when antenna is more than 150 meters lower in elevation than its radio horizon] The surface refractivity Ns is a function of temperature, pressure, and humidity, and decreases therefore with elevation. The effective earth radius a corresponding to the minimum monthly mean value of ns (fig 4.4-3) The median atmospheric attenuation, Aa, is determined as a function of carrier frequency and path length (fig 4.4-4)

Link Budget Parameters The time variability of basic transmission loss is expressed by empirical functions V(q) in decibels, where q denotes a fraction of all hours of an average year, such as 0.999, or the corresponding percentage such as 99.9%. Since there are 8760 hours in year of 365 days, q = O. 999 corresponds to all but approximately 9 hours of the year, and q = 0.9999 may be taken to represent all but hour, the function V(q) is a function of climate, path parameters, and carrier frequency

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